The Three-Dimensional Structure and Evolution of a Tornado Boundary Layer

1552 WEATHER AND FORECASTING VOLUME 28

KAREN A. KOSIBA AND JOSHUA WURMAN Center for Severe Weather Research, Boulder, Colorado

(Manuscript received 24 June 2013, in ﬁnal form 15 August 2013)

ABSTRACT

The finescale three-dimensional structure and evolution of the near-surface boundary layer of a tornado (TBL) is mapped for the first time. The multibeam Rapid-Scan Doppler on Wheels (RSDOW) collected data at several vertical levels, as low as 4, 6, 10, 12, 14, and 17 m above ground level (AGL), contemporaneously at 7-s intervals for several minutes in a tornado near Russell, Kansas, on 25 May 2012. Additionally, a mobile mesonet anemometer measured winds at 3.5 m AGL in the core flow region. The radar, anemometer, and ground-based velocity-track display (GBVTD) analyses reveal the peak wind intensity is very near the surface at ;5 m AGL, about 15% higher than at 10 m AGL and 25% higher than at ;40 m AGL. GBVTD analyses resolve a downdraft within the radius of maximum winds (RMW), which decreased in magnitude when 2 varying estimates for debris centrifuging are included. Much of the inflow (from 21to27ms 1) is at or below 10–14 m AGL, much shallower than reported previously. Surface outflow precedes tornado dissipation.

Comparisons between large-eddy simulation (LES) predictions of the corner ﬂow swirl ratio Sc and observed tornado intensity changes are consistent.

1. Introduction To observe the TBL with radar, it is necessary for that radar to be close to the tornado to mitigate the effects of The corner and boundary layer regions of tornadoes beam spreading and intervening obstructions (e.g., ter- (e.g., Lewellen 1976, 1993; Snow 1982; Kessler 1986, rain, structures, and foliage). On only rare occasions (e.g., 197–236; Davies-Jones et al. 2001) are the most difficult W07) are observations obtained ,10 m AGL. Ideally, and most critical to sample because they are in direct near-surface three-dimensional radar observations in contact with the underlying surface, cause damage, and combination with surface in situ one-dimensional tran- dictate the vortex structure at low levels and perhaps sects of the TBL would combine to provide a time-varying through a significant depth of the tornado. Although mo- three-dimensional mapping. However, in situ wind ob- bile radar observations of the tornado core flow have be- servations are exceedingly difficult and hazardous to ob- come more frequent (e.g., Wurman et al. 1996; Wurman tain due to the violence, unpredictable paths, and typically and Gill 2000, hereafter WG00; Bluestein et al. 2003; short lifespans of tornadoes (Wurman et al. 2013b, manu- Bluestein et al. 2004; Lee and Wurman 2005, hereafter script submitted to Bull. Amer. Meteor. Soc.). In the rare LW05; Wurman et al. 2007a, hereafter W07; Tanamachi instances that both in situ and low-level radar wind ob- et al. 2007; Kosiba et al. 2008, hereafter K08; Kosiba and servations have been obtained (e.g., W13), ground-relative Wurman 2010, hereafter KW10; Wakimoto et al. 2012, wind speeds near the surface, V , are comparable to or even hereafter W12; Wurman et al. 2013a, hereafter W13; g stronger than radar-measured winds, V , ;30 m AGL. Wurman and Kosiba 2013), they commonly are .40 m d Numerical simulations (e.g., Lewellen et al. 1997; AGL and inadequately sample the near-surface tornado Lewellen et al. 2000, hereafter L00; Lewellen and boundary layer (TBL) (i.e., the lower portion of the Lewellen 2007, hereafter LL07) and laboratory models boundary layer that may be impacted directly by fric- (e.g., Church et al. 1979) of tornadoes have been in- tional effects). strumental in understanding the TBL, but these results remain largely unverified observationally. Hoecker’s (1960) video analysis of the flow in a tornado attempted Corresponding author address: Dr. Karen A. Kosiba, Center for to quantify the near-surface structure of a tornado. Using , Severe Weather Research, 1945 Vassar Circle, Boulder, CO 80305. debris and cloud tags as tracers, radial inflow, Vr 0, was E-mail: [email protected] identified below 152 m AGL, and maximized at 53 m

DOI: 10.1175/WAF-D-13-00070.1

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AGL. Doppler on Wheels (DOW; Wurman et al. 1997; rapid tornado evolution during the several 10s of seconds Wurman 2001, 2008) radar data in one tornado did not between observations at the lowest and highest levels reveal inflow ;30 m AGL (WG00), but it was suggested (e.g., Wurman et al. 2007b). that centrifuging of debris (Dowell et al. 2005) may have masked the convergence signature. DOW data, taken at 2. Deployment overview and data ;10 and 14 m AGL from two different tornadoes (W07; Alexander and Wurman 2005, hereafter AW05), revealed During the 2012 season of the Radar Observations of 2 convergences of 0.10 and 0.06 s 1, respectively, suggesting Tornadoes and Thunderstorms Experiment (ROTATE; strong convergence (not fully masked by centrifuging) e.g., Wurman 1998, 2008) field campaign, three DOWs, near the surface. including the RSDOW, and in situ measurement teams LW05, KW10, W12, and W13 have used the ground- deployed in advance of potentially tornadic storms based velocity-track display (GBVTD) (Lee et al. 1999) moving toward Russell, Kansas, after dark on 25/26 May scheme to resolve three-dimensional tornado structure. 2012. At 0230 UTC 26 May, DOW71 was deployed at LW05 revealed inflow from z 5 0 to 1.15 km AGL in a 38.841958N, 98.85248W and the RSDOW deployed at large and violent tornado. W12 applied the GBVTD 38.856388N, 98.85458W, establishing a 1.6-km, dual- technique to DOW data from the second Verification Doppler baseline (Fig. 1). An instrumented mobile mes- of the Origins of Rotation in Tornadoes Experiment onet vehicle (P1) carrying ‘‘tornado pods’’ (not deployed) (VORTEX2;Wurmanetal.2012)inatornadoattwo moved north from DOW7. consecutive times. Initially, there was strong outflow, A tornado formed unexpectedly at 0235 UTC moving while 2 min later there was very weak inflow surrounding northeast, broadening, and impacting P1 at approxi- the tornado. An approximation for centrifuging of hy- mately 0238 UTC. The tornado contracted/reformed to drometeors weakened the initial outflow and strength- the north and then moved northeast, where P1 drove ened the later inflow. The large-eddy simulation (LES) of into its southwestern sector just after 0241 UTC. The Lewellen et al. (2008) demonstrated that small debris tornado continued north, with the center passing 30 m could alter the wind speeds and tornado structure near east of the RSDOW, resulting in generator failure and the surface. Using GBVTD and numerical simulations, ending RSDOW operations. Nolan (2013) emphasized the need to represent accu- The tornado transported a house with its resident,2 rately the low-level inflow and to account for debris located 30 m northeast of the RSDOW, about 30 m east- 3 centrifuging. The debris centrifuging velocity, Vcf,which ward, destroying it completely [10 degrees of damage depends on debris type, amount, density, shape, recycling, (DOD10) on the enhanced Fujita (EF) scale; Edwards electrical/scattering characteristics, etc., currently is un- et al. (2013); see Fig. 1]. A nearby house and several known, and can only be approximately accounted for in other structures were also damaged. At 0242:11 UTC, 21 4 radar-based analyses. Vg 5 43 m s was observed by P1 at 3.5 m AGL, which W13 combined in situ anemometer wind measure- experienced the weaker, western side of the tornado ments (in the same tornado analyzed by W12) at 3.5 m core flow. Maximum RSDOW-measured winds, Vd,were 2 AGL with Rapid-Scan DOW (RSDOW; Wurman and 64 m s 1 at 6 m AGL5 at 0240:53 UTC, and the peak ve- 2 Randall 2001) observations $30 m AGL to reconstruct locity difference across the vortex was 113 m s 1 at 6 m the low-level tornado vortex structure. At 3.5 m AGL, AGL at 0241:08 UTC. DOW7 observations depicted 21 strong radial inflow (Vr ;240 m s ) was present just a low-reflectivity eye and an intermittent debris ring outside the radius of maximum Vt (RMW), but at (Fig. 1). The RMW was typically about 50–70 m dur- ;30 m AGL, radar analyses revealed little to no inflow. ing the analysis period. The tornado dissipated at Integrated analyses revealed a divided vortex structure ;0243 UTC. with an axial updraft near the surface and a downdraft aloft. No data were available between 3.5 and 30 m AGL, so the details of the vertical profile of the winds in these 1 DOWs have 3-dB beamwidths of ;0.98, oversampled at 0.38– lowest, critical levels of the TBL are unknown. Peak 8 2 0.4 , gating at 25 m (RSDOW) and 30 m (DOW7). 5 1 2 anemometer-measured winds, Vg 58 m s ,weremore P1 crew discovered the resident ;100 s after the event, sitting intense than those measured by radar ;30 m AGL. on the rubble of the transported/destroyed house, suffering from DOW observations from other tornadoes also suggested lacerations and a broken collarbone; the crew assisted in her that the most intense velocities may occur ,30 m AGL extraction. 3 The National Weather Service (NWS) rated the tornado EF2. (W07). Except for W13, these previous radar-based 4 P1 hosts an R. M. Young 5103 propeller-type anemometer. analyses used conventionally scanned radar data, result- 5 Reported DOW observations height adjusted 13 m, accounting in limitations due to possible errors resulting from ing for antenna height AGL.

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FIG. 1. Moving clockwise from top left: path of the tornado and schematic core ﬂow areas (yellow line and circles) and radar-indicated centers (yellow dots) with DOW7, RSDOW, and P1 locations shown by red dots; photos of the foundation and rubble of a destroyed house; DOW7 reﬂectivity and velocity in hook echo and tornado; and 2 a schematic of vertical sampling by RSDOW and DOW7 (beam heights, m) with the location of P1’s 43.2 m s 1 in situ observation indicated.

The proximity of the RSDOW to the tornado (;130 m ground (simultaneous slices as low as 4, 6, 10, 12, 14, to the circulation center at the last data collection time, and 17 m AGL), well resolving the three-dimensional 0242:32 UTC) and six simultaneous radar beams resulted structure and evolution of the TBL for the ﬁrst time in mapping of the TBL with unprecedented spatial (25-m (Figs. 2 and 3). range and 3-m beamwidth with 1-m oversampling) and GBVTD analyses using 7-s RSDOW volumes temporal resolution (7-s volumes) and proximity to the from 0240:53 to 0242:25 UTC yielded independent

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FIG. 2. RSDOW Doppler velocity at six different GBVTD analysis times. (a)–(e) The second lowest elevation angle (7–11 m AGL at tornado) and (f) is at the highest elevation angle (17 m AGL at tornado). Times in hours (HH), minutes (MM), and seconds (ss) (HHMM: ss UTC) indicate the radar beam crossing through the tornado. Red dots indicate the location of the RSDOW. Tick marks indicate every 0.1 km. Yellow circles in (d),(e) show P1 (detected as moving clutter gates, conﬁrmed by GPS, and deleted). Wind barbs in (e) depict the 2 2 P1 in situ observations at 0241:14 UTC (long barb is 10 m s 1 and the short barb is 5 m s 1). Raw wind observation is shown in black. P1 location and wind vector adjusted for tornado translation between the radar and the anemometer observation (red).

6 three-dimensional wind fields at 14 times (Fig. 5). The 2 to 10 m, with only a slight reduction in Vt at grid sensitivity of the results to objective analysis parameters, spacing 5 10 m. Small changes in tornado center deter- lower boundary conditions, and errors in the center mination also did not impact the results substantially; location7 was explored. The vortex structure was not al- an alternate, no-slip, lower-boundary condition reduced 8 tered substantially by changes in the grid spacing from Vt below the lowest observation level, but did not alter the vortex structure. The sensitivity to a simple inclusion of debris centrifuging is discussed below. 6 RSDOW data were objectively analyzed onto a Cartesian grid using a Barnes scheme (Barnes 1964), grid spacing (radius of in- 3. Results and discussion fluence) of 5 (10) m and 2 (3) m in the horizontal and vertical di- 9 rections, respectively. Tornado translational motion was subtracted The maximum Vd from each RSDOW scan and ob- from Vd. Tornado centers were vertically aligned, eliminating tilting jectively analyzed grid was normalized to V (10 m AGL). errors, but not correcting for flow asymmetries. Vertical winds (w) d were derived by the upward integration of the continuity equation, Peak Vd was observed at the lowest radar-observed level, 2 assuming w(z 5 0) 5 0ms 1 and free slip. 7 Errors in vortex center location were ,7m. 8 9 Grid spacing (d) 5D/2.5 (where D is the raw data spacing) It is likely that Vg . Vd because Vd only captures the compo- (Koch et al. 1983). nent of motion toward–away from the radar.

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FIG. 3. RSDOW Doppler velocity at six simultaneously observed levels through the tornado at 0242:11 UTC. Fields and annotations are as in Fig. 2. The most intense Doppler velocities are observed at the lowest elevations. The range to the ﬁrst useful gate is less in higher- elevation beams. Heights of tornado center are indicated in red.

4–6 m AGL, at all times except 0241:14 and 0241:21 UTC, consistent with or slightly higher than observational- 11 when the maximum was observed at 10 m AGL (Fig. 4). angle-adjusted Vd at 5 m AGL over P1 (Fig. 2e), cor- At most times (and in the median and mean profiles), peak roborating that the maximum Vg occurred near or Vd decreased ;15% from 5 to 10 m AGL, then gradually possibly below 5 m AGL. Critically, this result shows decreased another ;10% up to 25–40 m AGL, matching that radar observations of Vd at ;50 m AGL (e.g., the trend noted from 14 to 100 m AGL in W07, and con- WG00, AW05, W07, W13) are likely underestimations sistent with Vg (3.5 m AGL) . Vd (30 m AGL) reported in of the Vg typically occurring at 5–10 m AGL. How- W13. This indicates that the ‘‘nose’’ (maximum) of Vg was ever, comparing radar-measured Vd to hypothetical very near 5 m AGL and that the true shallow TBL radial ‘‘standard’’ 3-s-averaged anemometer-measured Vg is inflow was mapped here in detail for the first time. The problematic.12 strongest inflow may even exist below 5 m AGL, where At all analysis times, GBVTD results revealed a further frictional reduction of Vt couldleadtoanimbal- two-celled tornado vortex structure, with a downdraft ance in the pressure-gradient force, causing enhanced in- inside the RMW extending from the top of the domain

flow. Temporal variations in Vd likelywereduetotrue to the surface. Near-surface inflow, just outside of the changes in vortex intensity as the tornado is observed by both the DOW7 and RSDOW to rapidly strengthen then rapidly dissipate. In situ anemometer observations from 21 11 P1 is visible as moving ground clutter in the lowest RSDOW P1, with peak Vg 5 43.2 m s at the edge of the western 10 sweeps. (weak) edge of the core flow region, were roughly 12 Radar measurements are instantaneous and represent reflectivity-weighted averages of scatterer (rain/debris, with associated terminal/centrifuging velocities) motion, usually determined 10 P1 drove into the western side of the tornado after the tornado using pulse-pair or spectrally based signal processing techniques, center had moved east of the road. over spatial volumes not equal to 3-s air parcel trajectories.

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FIG. 4. (top) Maximum RSDOW Doppler velocity in the tornado as a function of height normalized by the 10 m AGL value and (bottom) maximum objectively analyzed RSDOW Doppler velocity as a function of height normalized by the 10 m AGL value for all 14 RSDOW volumes (time labels HMMss UTC, where H indicates hours). Stippled and solid lines depict the median and the mean for all times, respectively. Most intense winds are observed near 5 m AGL, decreasing about 15% by 10 m AGL, then decreasing about another 10% from 10 to 40 m AGL.

2 RMW, was present in all but the last three analysis times of 42.9 m s 1 from 2818 (Fig. 2), suggesting slight inﬂow,

(Figs. 5 and 6). Maximum inflow occurred at 0240:53 UTC, Vr , 0, while the GBVTD at this time suggests slight near the time of maximum Vd and Vt. At 0240:53 UTC, outflow, Vr . 0 (Figs. 5 and 6). This discrepancy could 21 Vr ,21ms was present # 14 m AGL, while Vr , be caused by inadequate compensation for debris centri- 2 25ms 1 was confined to #8 m AGL, with the strongest fuging, errors in correcting for tornado movement, asym- 21 inflow (Vr of approximately 27ms )at5mAGL.P1 metries in the tornado, stronger inflow ,5 m AGL, errors observations at 0241:14 UTC, adjusted for tornado trans- in the wind or radar measurements, or a combination of lation and motion, result in a tornado-relative velocity these factors.

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21 FIG. 5. GBVTD winds at (top) 0240:53, (middle) 0241:36, and (bottom) 0242:11 UTC with (left) no centrifuging and (right) an 8 m s centrifuging estimation. Colored contours depict the tangential velocity Vt, vectors depict the secondary circulation (Vr, w), and white line 2 contours depict the angular momentum (3103 m2 s 1). Tick marks along the right axes denote the heights of RSDOW sweeps through the 2 center of the tornado. The 0242:11 UTC analysis is just prior to the P1 in situ observation of 43.2 m s 1.

The value of Vt was maximum in the TBL, below ;6m and consistent with the values presented in W12 and 21 AGL (Fig. 6). By 0241:00 UTC, the depth of the inflow Dowell et al. (2005), Vc 5 8ms was used in this study 21 layer (Vr ,21ms ) had decreased to 10 m AGL and since this was a weak tornado and likely only hydro- 21 13 the layer containing Vr ,24to25ms decreased to meteors and small debris, such as dirt, gravel, and grass ,6 m AGL. From 0241:00 to 0241:22 UTC, the depth of were present throughout the GBVTD analysis interval 14 the inflow layer was ;10 m AGL, and Vr and Vt gener- as the tornado crossed open farm and grassland prior ally decreased in magnitude. At 0241:29 UTC, there was to impacting the structures near the RSDOW. Including a brief increase in the Vr , 0 and Vt, subsequently fol- an estimate for debris centrifuging moved the location lowed by a decrease in Vt until 0242:11 UTC, when Vt of maximum convergence inward (Fig. 6) and caused the increased until the end of the analysis. Although Vt in- weak central downdraft near the surface to become creased from 0242:11 to 0242:25 UTC, outflow Vr . 0was a weak central updraft at 0241:22–0241:43 and 0241:57– present outside the RMW and the tornado dissipated 0242:04 UTC. Indeed, with the inclusion of a simple approximately 60 s later. Strong Vt immediately prior to debris bias, the inward progression of the radial winds is tornado dissipation has been documented before (e.g., consistent with the LES results of LL00. The sign of Vr WG00, Kosiba et al. 2013). outside of the RMW was not changed by the inclusion of Since there is not adequate information on precisely how debris can bias Doppler velocity measurements, an exact quantification of debris centrifuging is beyond the 13 Since the observations were close to the surface, dirt, gravel, scope of this study. However, using the results of Dowell and/or grass likely were appreciable scatter types in the radar sample volumes. The in situ P1 crew did not report airborne debris hitting et al. (2005) and W12, Nolan (2013) provides a simple their vehicle. estimate of debris-centrifuging biases on retrieved axi- 14 The surface roughness length was approximated as 0.1 m, char- symmetric winds. Following Nolan (2013) [Eq. (3.1)], acteristic of ‘‘openly rough’’ terrain (Davenport et al. 2000).

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FIG. 6. Hovmoller€ diagrams of the axisymmetric horizontal winds in the TBL as a function of radius and time (top left) with no 21 centrifuging, and 4, 8, and 12 m s Vcf at 4 m AGL. Colored contours depict the tangential velocity Vt and radial inflow (outflow) Vr is denoted by solid (stippled) lines. Tick marks along the right axes denote times of RSDOW volumes. A downdraft/outflow is present inside the RMW at all times with no centrifuging and only at the early times when centrifuging is included. Inflow outside of the RMW is present 21 through 0242:11 UTC, with outflow afterward, in all analyses. The location and time of the P1 in situ observation (Vr 524.3 m s and 21 Vt 5 42.9 m s ) are shown with a white dot. debris (Fig. 5). Since one unknown in accounting for The depth of the inflow layer was much shallower than debris centrifuging is the size, shape, and density dis- has been reported in previous studies (e.g., LW05, K08, tribution of the debris–hydrometeor mix, and hence Vcf, KW10, W12), but these results were based completely or 21 sensitivity of the results to varying Vcf (4 and 12 m s ) primarily on data well above the shallow TBL revealed was explored (Figs. 6c and 6d). As expected, the higher here. W12, KW10, K08, and LW05 employed vertical (lower) value increased (decreased) inflow and allowed grid spacings of 50, 40, 25, and 30 m, respectively, so these the inflow to penetrate farther (less far) inward. The likely did not resolve very-near-surface inflow, but in- central updraft–downdraft responded according to changes stead captured the large-scale inflow associated with the in the inflow. wind field outside the core flow region of the tornado, or

Unauthenticated | Downloaded 09/24/21 07:34 PM UTC 1560 WEATHER AND FORECASTING VOLUME 28 a smoothed representation of inflow below their lowest consistent with LES results. A two-celled vortex structure analysis level. The weaker inflow revealed here compared is revealed by GBVTD analysis without the inclusion of to the analyses of LW05, K08, KW10, and W13 may be debris centrifuging, and outflow outside the RMW was due to the resolution of the true TBL or because the observed just prior to tornado dissipation. Inclusion of current tornado was weaker and short lived, with low- varied estimates for debris centrifuging changed weak level inflow not conducive to sustaining an intense, long- downdrafts to very weak updrafts inside the RMW and lived vortex (L00). the flow direction outside of the RMW was unaltered. In the LESs of L00 and LL07, a corner flow swirl The most intense winds in the tornado occurred ;5m 15 ratio Sc has been defined to characterize the impacts of AGL, extending surfaceward the results of previous near-surface, tornado-scale flow on vortex structure and studies sampling above the TBL (e.g., W05, W07) or intensity. While Sc does not replace the outer-scale swirl sparsely within the TBL (W13). Radar-observed Vd afew ratio So (e.g., Church et al.1979; Lee and Wurman 2005), 10 s of meters AGL are shown to be representative or Sc underscores the importance of near-surface flow even underestimates of Vg approximately ,10 m AGL. 16 structure, which is not captured by So. At the ‘‘optimal’’ More observations are needed over a range of vortex Sc value (Sc 5 0.70–1.38; LL07), the ratio of the average structures and intensities to characterize the TBL more maximum swirl velocities (Vmax) in the surface layer to generally. the average swirl velocities above the surface layer (Vc)is 2.5 (L00). In the current analysis, values of Vmax (z 5 4m Acknowledgments. Analysis supported by NSF-AGS- AGL)/Vc (z 5 20 m AGL) , 1.5. The highest values 0910737 and DOWs by NSF-AGS-0801041. We thank (Vmax/Vc 5 1.37–1.47) occurred at the first three anal- Curtis Alexander, Paul Robinson, and Rachel Humphrey. ysis times. The lowest values (;1.0) were observed at 0241:22, 0242:04, 0242:18, and 0242:25 UTC, when the REFERENCES angular momentum outside of the RMW was reduced in the TBL, perhaps indicating an influx of far-field lower Alexander, C., and J. Wurman, 2005: The 30 May 1998 Spencer, angular momentum fluid near the surface, decreasing South Dakota, storm. Part I: The structural evolution and environment of the supercell tornadoes. Mon. Wea. Rev., 133, the tornado intensity. Using quantities available in the 72–96. GBVTD domain, and only for times when Vr , 0was Barnes, S. L., 1964: A technique for maximizing details in numer- 17 3, observed, Sc 1, so Sc would have to either decrease ical weather-map analysis. J. Appl. Meteor., 396–409. (assuming an unchanged flow aloft) or stayed fixed (if the Bluestein,H.B.,W.-C.Lee,M.Bell,C.C.Weiss,andA.L.Pazmany, core radius aloft was reduced) in order for the vortex to 2003: Mobile Doppler radar observations of a tornado in 18 a supercell near Bassett, Nebraska, on 5 June 1999. Part II: intensify. Tornado-vortex structure. Mon. Wea. Rev., 131, 2968–2984. ——, C. C. Weiss, and A. L. Pazmany, 2004: The vertical structure 4. Conclusions of a tornado: High-resolution, W-band, Doppler radar observations near Happy, Texas, on 5 May 2002. Mon. Wea. Rev., 132, The TBL and inflow layer were much shallower than 2325–2337. Church, C. R., J. T. Snow, G. L. Baker, and E. M. Agee, 1979: previously documented, confined below 10–14 m AGL. Characteristics of tornado-like vortices as a function of swirl While it is possible that more intense tornadoes may ratio: A laboratory investigation. J. Atmos. Sci., 36, 1755–1776. have deeper boundary and inflow layers, it is likely that Davenport, A. G., C. S. B. Grimond, T. R. Oke, and J. Wieringa, prior observational studies characterized the inflow layer 2000: Estimating the roughness of cities and sheltered country. of the larger-scale circulation, not of the tornado itself. Preprints, 12th Conf. on Applied Climatology, Asheville, NC, Amer. Meteor. Soc., 96–99. Estimation of Sc predictions from the current data are Davies-Jones, R. P., R. J. Trapp, and H. B. Bluestein, 2001: Torna- does and tornadic storms. Severe Convective Storms, Meteor. Monogr., No. 50, Amer. Meteor. Soc., 167–221. 15 Here, Sc 5 rcG‘/Y, where rc is a characteristic radius of Dowell, D. C., C. R. Alexander, J. M. Wurman, and L. J. Wicker, Vt(max), G‘ is the ambient angular momentum, and Y is the de- 2005: Centrifuging of hydrometeors and debris in tornadoes: pleted angular momentum flux in the surface layer. Radar-reflectivity patterns and wind-measurement errors. Mon. 16 123, Note that So characterizes the flow in which the tornado forms. Wea. Rev., 1501–1524. Both So and Sc are difficult to define in nature since flow parameters Edwards, R., J. G. LaDue, J. T. Ferree, K. Scharfenberg, C. Maier, are not easily defined. In addition, So cannot be approximated in and W. L. Coulbourne, 2013: Tornado intensity estimation: the current study since the analysis domain is too small to define the Past, present, and future. Bull. Amer. Meteor. Soc., 94, 641–653. large-scale flow in which the tornado is embedded. Hoecker, W. 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